Front
You start in the upper left corner of the map. Snakes and Spiders will begin to appear. Head right and jump the gap to reach door A.
Door A
In this one-room doorway, you will find the 
Hammer. Be sure to take it before backing out of the room and continuing on your way. Drop down to the platform below and head to door B.
Door B
There are two rooms behind door B. The first room that you come to has a 
Keyring. Take it and you will now be capable of holding two keys at a time. The room beyond it contains a hint giving safe, but it will cost you a key to open the safe and read the hint. If you would rather not use up a precious key, highlight the space between the parentheses to read the hint: (FIND THE GOONIES WITH THE MAGIC LOCATOR DEVICE.) A hole in the ceiling above can only be accessed once you have the ladder.
Return to the house outside, and continue running right. Climb down two ladders to reach the white basement level below. Once you arrive, begin heading left. It does not matter if you take the upper path or the lower path, whichever is safest. One of the Fratelli brothers will appear and try to stop you with his gun. Hit him twice to knock him unconscious. You will soon reach door C. However, if you would like to get an easy Slingshot, continue moving to the left to door D.
Door C
Behind door C is a single room with a set of doors in the back. The room contains a "Magic Locator Device" which can be used to determine the location of a nearby Goonie. If you use it, you will discover that a Goonie is located above you in the back layer of the house. Head forward through the opposite door, and you will arrive at door C in the back layer of the house.
Door D
This door is entirely optional. In the first room, you will find a 
Slingshot, which you can take, and it will always be there when you are out of Slingshot stones. In the room beyond the Slingshot, you will find an old lady who will inform you that she has trouble seeing without glasses, and asks you if you have any. (Even if you do, using them here does nothing.) When you are finished here, back out and return to door C.
Back
When you arrive in the back layer, it is not required, but worthwhile to explore the area below door C. Start by heading right, ride the moving platform down, and climb down the ladder to the section below. Continue right and ride the two moving platforms until you reach door E in the upper right corner of the section.
Door E
You begin in the center room, from you can you go to the right or left. The room to the left has a safe with a hint that you must use a key to read. Highlight the space between the parentheses to read the hint: (YOU'LL GET EXTRA ENERGY FOR SAVING GOONIES.) The room to the right will appear empty, but if you hit the wall with your fist, you will discover the first of five Fire Boxes. This box will equip you with, and allow you to store up to 5 Molotov Cocktails. When you're done here, return to the center room and back out to the basement level.
Return to your arrival point at door C, and climb up the ladder to the portion of the house above. When you reach this floor, you can climb up the ladder and head to the right to make your way to Door G, or you can run to the left end and investigate Door F.
Door F
You won't find much of interest behind this door at such an early point in the game. When you arrive, a man will greet you and inform you that this is a warp zone. If you investigate the room to the left, you won't immediately notice anything. However, if you use the Hammer, and hit the ceiling, you can create a hole. Without a ladder, you will have no choice by to back out and return to the house.
Door G
When you enter the room, all you can see if the door to the right. However, if you hit the wall with your fist, you will expose a Bomb Box which will give you the ability to store up to 5 Bombs, and give you a full supply. Enter the room to the right, and again, the room will appear vacant. However, the Magic Locator Device insists that this is where a Goonie is being held. If you use your Hammer and hit the back wall, you will expose a door. Go through the door, and there you will find your first Goonie. Use one of your keys to open the cell and rescue the Goonie. You will now have three bars of health instead of two.
With your first Goonie rescued, it's time to move on to a new area and find the second Goonie. The only area left to discover is the lower basement level of the front layer. Return to the front layer through door C, and head right until you see a ladder that extends down below. Climb down the ladder, and use the moving platforms to make your way to the left. Enter door H.
Door H
The old man inside of this single room informs you that it is a warp zone, and indeed it is. It will take you to the red cavern area where you will begin your quest for the second Goonie.